In radio communication, information to be transmitted is converted in a modulator to a high-frequency radio signal which is transmitted via a communication channel, i.e. a radio channel, to a receiver. In the receiver, the received radio-frequency signal is demodulated, wherein the aim is to use the received high-frequency signals to form the information which substantially corresponds to the original information.
However, this communication based on radio signals is susceptible to noise which can be due to e.g. high-frequency signals caused by other electric devices, changes in the conditions of the communication channel, bars affecting the propagation of radio signals, such as buildings, trees, topography, etc. Methods have been developed to reduce the effect of such noise. In systems, in which the modulation method used is based on phase shift (M-ary Phase Shift Keying, MPSK), receivers commonly apply a channel estimator and a channel equalizer to compensate for changes caused by the communication channel in the signal. The aim of a channel estimator is to determine the transfer function of the communication channel effective on the propagation of the radio signal, wherein it is possible in the channel equalizer to make a correction in the received signal on the basis of this determined transfer function. As the channel equalizer, e.g. the maximum likelihood sequence equalizer (MLSE) and the Viterbi algorithm can be used. With such an arrangement, the effects of the communication channel can be compensated for, to at least some extent. However, such an arrangement involves e.g. the problem that the complexity of the system increases exponentially the higher, the more channel taps are determined from the transfer function in the channel estimator. On the other hand, the more channel taps can be estimated, the better it is possible to compensate for distortions in the signal which are due to e.g. multipath propagation. In a formula, the complexity of the system can be depicted by MH, in which H is the number of estimated channel taps and M is the number of different phase-shift alternatives to be used in the modulation.
As the radio signal is reflected from obstacles, such as buildings, vegetation, topography, etc., it causes so-called multipath propagation, wherein the same signal comes to the receiver along several different paths. Since these different signal paths can have different lengths and they are longer than the distance travelled by the signal directly from the transmitter to the receiver, the signals propagating along different paths are received by the receiver at different times. Furthermore, such a multipath-propagated signal can be stronger than the directly propagated signal, wherein signals which have come to the receiver along different paths cannot be differentiated from each other solely on the basis of the signal strength. Particularly in said phase modulation, multipath propagation has a significant effect on the performance of the receiver. In principle, for example four-tap estimation can be used to compensate for four multipath-propagated signals which come to the receiver at different times. However, receivers of prior art are thus very complex compared to a situation in which for example one-tap estimation is used.
The following is a brief discussion of the transmission of binary information by using phase shift keying. Let us fix the time index t to t=τ+tΔτ in which Δτ is the symbol transmission interval. The symbol S(Bt) corresponds to three bits Bt=└bt,1,bt,2,bt 3┘ at time t(bt,kε{0,1}), when 8PSK modulation is applied. Thus, the symbol generator can be presented by the formulaS(B)=a2(1−b1)b2b3+a4(1−b1)b2(1−b3)+a6(1−b1)(1−b2)(1−b3)+a8(1−b1)(1−b2)b3+a10b1(1−b2)b3+a12b1(1−b2)(1−b3)+a14b1b2(1−b3)+a16b1b2b3  (1)where a=et2π/16.
The symbols are transmitted to the communication channel. In the receiver, the signal to be received at time t is
                              r          t                =                                            ∑                              s                =                0                                            H                -                1                                      ⁢                                                  ⁢                                                            h                  ~                                s                            ⁢                              S                ⁡                                  (                                      B                                          t                      -                      s                                                        )                                                              +                      n            t                                              (        2        )            in which {tilde over (h)}s indicates H channel taps and nt indicates channel noise which is assumed to be Gaussian noise.
An optimal channel equalizer would be one that maximizes the likelihood function. If it is assumed that the noise mixed with the signal is Gaussian noise and the probability of all the symbols S is equal, then the maximization of the likelihood functions corresponds to the minimization of the function
                              f          ⁡                      (            B            )                          =                              ∑                          t              =              0                        T                    ⁢                                          ⁢                                                                                    r                  t                                -                                                      ∑                                          s                      =                      0                                                              H                      -                      1                                                        ⁢                                                                          ⁢                                                            h                      s                                        ⁢                                          S                      ⁡                                              (                                                  B                                                      t                            -                            s                                                                          )                                                                                                                                2                                              (        3        )            in which S(B) is the symbol corresponding to bits B, hs are the estimated channel coefficients, and r is the received signal. Consequently, the problem is to find the bits B after receiving r and estimating h. In the above formula, T+1 is the number of transmitted symbols, H indicates the number of channel taps, and s is the tap index. To simplify the notations, time index t indicates the value u+tΔu in which u is time and Δu is the sampling interval. The function f can be minimized by using the Viterbi algorithm. However, the problem is that the complexity of the Viterbi algorithm increases exponentially as the function of the number of channel taps H, as already mentioned above. Another method is to first use a prefilter to reduce the number of channel taps to for example two and, after this, to apply the Viterbi algorithm to maximize the likelihood function. However, this method has the drawback that the result depends e.g. on the quality of the prefilter and the type of the channel. One method applying the Viterbi algorithm is based on the use of a delayed decision-feedback sequence estimator (DDFSE). In this method, the Viterbi algorithm is applied in the feedback filter. The performance of such a sequence estimator is affected by e.g. the number of states used in Trellis coding. If the number of states is sufficiently large, the performance is close to the optimum, but the estimator is thus very complex. Such an estimator operates the better, the smaller the phase shift in the channel, wherein the estimator requires a filter whereby this phase shift can be reduced.